本文之研究目的為開發混合共振模態於壓電體聲波模態陀螺儀之新穎設計。利用 COMSOL Multiphysics 軟體中的有限元素分析進行陀螺儀結構的優化，且與已發表 的高頻壓電共振式陀螺儀相比，由旋轉所引發的科里奧利力也可有效地偵測。 模擬結果顯示了混和式共振式陀螺儀，其品質因子為 10000，且靈敏度 為 12.26 nA◦ /s 並擁有高於 5000 ◦ /s 的線性動態範圍。而環形陀螺儀的設計目的為 利用薄膜壓電感測以實現 (n = 3) 的次橢圓模態。本研究的元件藉由商用製程 （PiezoMUMPs與MEMSCAP） 實 (100) 單晶矽 10 毫米的結構厚度，並於單晶矽表 面沉積一層厚度為 0.5 毫米的氮化鋁 （AlN）薄膜與作為頂電極厚度為 1 毫米的鋁 （Al） 層。 本研究中所提出的兩種陀螺儀元件，其諧振特性可透過網絡分析儀測得。由量 測結果可知，儘管所提出的混合共振式陀螺儀在單晶矽表面上的驅動與感測方向並 未與 對齊，且驅動模態與感測模態之間存在 11.7 kHz 的頻率差異，此元件 在空氣中仍擁有超過 1000 的品質因子且共振頻率約為 10.8 MHz。 綜合模擬與量測 的頻率響應，混和共振式陀螺儀相較於頂電極採用常規配置以激發 n = 3 模態腔體 共振的環形陀螺儀具有較佳的表現。 藉由鎖相放大器閉迴路控制與開迴路讀取組態以完成角速度的測量。混合共 振陀螺儀已成功反映了對科里奧利力的敏感性，其性能表現在模態不匹配的操 作下，未進行解調前約能在 ±95 ◦ /s 的動態範圍內擁有約 787 pA/◦ /s 的靈敏度與 0.38 ◦ /s/√ Hz 的解析度。並於短時距測量下擁有 0.167 ◦ /s 的偏誤不穩定度與 110.6 ◦ / √ h 的角度隨機遊走。與離散放大器電路結合後所測得的輸出雜訊水平為 32.61 µV/√ Hz。

The intent of this research is to introduce a novel design for high frequency piezoelectric bulk acoustic wave (BAW) gyroscope using hybrid resonance modes of length extensional vibration mode and secondary elliptical mode (n = 3). Finite element analysis (FEA) of COMSOL Multiphysics software has been used for optimizing structures, and demonstrating the effective detection of Coriolis force due to rotation in comparison with reported high-frequency piezoelectric resonator gyroscopes.

Simulation shows that this device has a sensitivity of 12.26 nA◦ /s with the linear dynamic range greater than 5000 ◦ /s at Q = 10000. An annular gyroscope is also designed for the purpose of reference about n = 3 mode by thin film piezoelectric transduction. The commercial process (PiezoMUMPs, MEMSCAP inc.) is selected for the fabrication with device structural thickness of 10 µm of (100) single crystal silicon (SCS), 0.5 µm thick aluminum nitride (AlN) thin film deposited on SCS surface, along with 1 µm thick aluminum (Al) top electrode.

The resonance characteristics of two gyroscopes are first measured using network analyzer. In according with the test results, the frequency split between drive and sense modes of hybrid resonance gyroscope is 11.7 kHz, even though, the drive direction and sense direction of referred gyroscope have not been aligned to on the surface of SCS. It obtains quality factor exceeding 1000 in air with the resonance frequency of about 10.8 MHz. The conventional placement of electrodes on top of an annular gyroscope to stimulate the resonance of n = 3 mode has achieved a poor performance based on frequency response from simulation and experimental measurement.

The driven closed-loop control and open-loop readout configuration of a digital lock-in amplifier are utilized for angular rate measurement. Hybrid resonance gyroscope has been ii firstly demonstrated to be sensitive to Coriolis force, and the gyroscope has a scale factor of about 787 pA/◦ /s in a dynamic range of ±95 ◦ /s with a resolution of 0.38 ◦ /s/√ Hz under the mode-mismatch operation before demodulation. A zero bias instability of 0.167 ◦ /s and an angle random walk of 110.6 ◦ / √ h have been attained for short-time measurement. The measured output noise floor that compromises of a discrete amplifier circuit is 32.61 µV/√ Hz.

[1] J. Bernstein, S. Cho, A. King, A. Kourepenis, P. Maciel, and M. Weinberg, “A micromachined comb-drive tuning fork rate gyroscope,” in [1993] Proceedings IEEE Micro Electro Mechanical Systems. IEEE, 1993, pp. 143–148.

[2] M. Lutz, W. Golderer, J. Gerstenmeier, J. Marek, B. Maihofer, S. Mahler, H. Munzel, and U. Bischof, “A precision yaw rate sensor in silicon micromachining,” in Proceedings of International Solid State Sensors and Actuators Conference (Transducers’ 97), vol. 2. IEEE, 1997, pp. 847–850.

[3] J. Classen, J. Frey, B. Kuhlmann, P. Ernst, and R. Bosch, “Mems gyroscopes for automotive applications,” in Advanced Microsystems for Automotive Applications. Springer, 2007, pp. 291–306.

[4] F. Ayazi and K. Najafi, “A harpss polysilicon vibrating ring gyroscope,” Journal of microelectromechanical systems, vol. 10, no. 2, pp. 169–179, 2001.

[5] H. Johari and F. Ayazi, “Capacitive bulk acoustic wave silicon disk gyroscopes,” in 2006 International Electron Devices Meeting. IEEE, 2006, pp. 1–4.

6] M. Hodjat-Shamami, A. Norouzpour-Shirazi, R. Tabrizian, and F. Ayazi, “A dynamically mode-matched piezoelectrically transduced high-frequency flexural disk gyroscope,” in 2015 28th IEEE International Conference on Micro Electro Mechanical Systems (MEMS). IEEE, 2015, pp. 789–792.

[7] K. Jose, W. Suh, P. Xavier, V. Varadan, and V. Varadan, “Surface acoustic wave mems gyroscope,” Wave motion, vol. 36, no. 4, pp. 367–381, 2002.

[8] Z. Song, X. Chen, S. Huang, Y. Wang, J. Jiao, and X. Li, “A high-sensitivity piezoresistive gyroscope with torsional actuation and axially-stressed detection,” in SENSORS, 2003 IEEE, vol. 1. IEEE, 2003, pp. 457–460.

[9] J. Georgiou and C. M. Andreou, “Hybrid mems microfluidic gyroscope,” Feb. 15 2018, US Patent App. 15/688,052.

[10] O. J. Woodman, “An introduction to inertial navigation,” University of Cambridge, Computer Laboratory, Tech. Rep., 2007.

[11] C. Acar and A. Shkel, MEMS vibratory gyroscopes: structural approaches to improve robustness. Springer Science & Business Media, 2008.

[12] H. Wen, A. Daruwalla, Y. Jeong, P. Gupta, J. Choi, C.-s. Liu, and F. Ayazi, “A high-performance single-chip timing and inertial measurement unit with robust mode-matched gyroscopes,” in 2018 IEEE Micro Electro Mechanical Systems (MEMS). IEEE, 2018, pp. 105–108.

[13] D. Serrano, R. Lipka, D. Younkin, P. Hrudey, J. Tovera, A. Rahafrooz, M. Zaman, S. Nagpal, I. Jafri, and F. Ayazi, “Environmentally-robust high-performance tri-axial bulk acoustic wave gyroscopes,” in 2016 IEEE/ION Position, Location and Navigation Symposium (PLANS). IEEE, 2016, pp. 5–8.

[14] D. E. Serrano, M. F. Zaman, A. Rahafrooz, P. Hrudey, R. Lipka, D. Younkin, S. Nagpal, I. Jafri, and F. Ayazi, “Substrate-decoupled, bulk-acoustic wave gyroscopes: Design and evaluation of next-generation environmentally robust devices,” Microsystems & Nanoengineering, vol. 2, no. 1, pp. 1–10, 2016.

[15] W.-k. Sung, M. Dalal, and F. Ayazi, “A 3mhz spoke gyroscope with wide bandwidth and large dynamic range,” in 2010 IEEE 23rd International Conference on Micro Electro Mechanical Systems (MEMS). IEEE, 2010, pp. 104–107.

[16] H. Wen, A. Daruwalla, C.-S. Liu, and F. Ayazi, “A high-frequency resonant framed-annulus pitch or roll gyroscope for robust high-performance single-chip inertial measurement units,” Journal of Microelectromechanical Systems, vol. 27, no. 6, pp. 995– 1008, 2018.

[17] R. Tabrizian, M. Hodjat-Shamami, and F. Ayazi, “High-frequency aln-on-silicon resonant square gyroscopes,” Journal of microelectromechanical systems, vol. 22, no. 5, pp. 1007–1009, 2013.

[18] M. Hodjat-Shamami, A. Norouzpour-Shirazi, and F. Ayazi, “Eigenmode operation as a quadrature error cancellation technique for piezoelectric resonant gyroscopes,” in 2017 IEEE 30th International Conference on Micro Electro Mechanical Systems (MEMS). IEEE, 2017, pp. 1107–1110.

[19] S. W. Yoon, S. Lee, and K. Najafi, “Vibration-induced errors in mems tuning fork gyroscopes,” Sensors and Actuators A: Physical, vol. 180, pp. 32–44, 2012.

[20] S. D. Senturia, Microsystem design. Springer Science & Business Media, 2007.

[21] M. Zaman and S. Rao, “Baw gyroscope technology positioned to transform inertial mems applications,” Qualtre, Inc ´, pp. 1–7, 2014.

[22] B. A. Auld, Acoustic fields and waves in solids. Рипол Классик, 1973.

[23] K. Tsubouchi, K. Sugai, and N. Mikoshiba, “Aln material constants evaluation and saw properties on aln/al2o3 and aln/si,” in 1981 Ultrasonics Symposium. IEEE, 1981, pp. 375–380.

[24] J. Zou, “High-performance aluminum nitride lamb wave resonators for rf front-end technology,” Ph.D. dissertation, UC Berkeley, 2015.

[25] M. Vijaya, Piezoelectric materials and devices: applications in engineering and medical sciences. CRC press, 2012.

[26] H. Bhugra and G. Piazza, Piezoelectric MEMS resonators. Springer, 2017.

[27] J. Yang and G. A. Maugin, Mechanics of electromagnetic solids. Springer Science & Business Media, 2013, vol. 3.

[28] J. Burdess and T. Wren, “The theory of a piezoelectric disc gyroscope,” IEEE transactions on aerospace and electronic systems, no. 4, pp. 410–418, 1986.

[29] J. Yang, C. Si, G. Han, M. Zhang, J. Ning, Y. Zhao, F. Yang, and X. Wang, “A decoupling design with t-shape structure for the aluminum nitride gyroscope,” Micro-machines, vol. 10, no. 4, p. 244, 2019.

[30] Y. Kagawa, T. Tsuchiya, and T. Kawashima, “Finite element simulation of piezoelectric vibrator gyroscopes,” IEEE transactions on ultrasonics, ferroelectrics, and frequency control, vol. 43, no. 4, pp. 509–518, 1996.

[31] K. G. Allen Cowen, Greg Hames and B. Hardy, PiezoMUMPs Design Handbook. MEMSCAP Inc, 2019.